The longer leg of a right triangle 3 cm is longer than the shorter leg. The hypotenuse is 6cm longer than the shorter leg. Find the side lengths of the triangle.

Answer 1

s² + (s + 3)² = (s + 6)²

Can you solve for s and answer?

Answer 2

Let s = the short side.

Then the longer leg = (s+3) and the hypotenuse = (s+6)

To find the side lengths, you will use the relationship of Pythagorean Theorem (a²+b²=c²)

1) Plug in what we know:

s² + (s + 3)² = (s + 6)²

2) multiply (s + 3)² and (s + 6)² in the equation:

s² + s² + 6s + 9 = s² + 12s +36

3) combine like terms and move everything over to one side/ set equation equal to 0:

2s² + 6s + 9 = s² + 12s +36

-s² -s²

s² + 6s + 9 = 12s +36

-12s -12s

s² - 6s + 9 = 36

-36 -36

s² - 6s - 27 = 0

4) this is a quadratic so we can factor it out. We need two numbers that add up to -6s and multiply to -27

(s - 9)(s+3) = 0

5) use the zero product property and set each factor equal to 0:

s - 9=0 s + 3=0

s = 9 and s = -3